We describe the construction and general features of VIPERS, the VIMOS Public Extragalactic Redshift Survey. This ESO Large Programme is using the Very Large Telescope with the aim of building a spectroscopic sample of ~100 000 galaxies with isubAB< 22.5 and 0.5 <z< 1.5. The survey covers a total area of ~24 degsup 2 within the C FHTLS-Wide W1 and W4 fields. Here we present the survey design, the selection of the source catalogue and the development of the spectroscopic observations. We discuss in detail the overall selection function that results from the combination of the different constituents of the project. Benefiting from the combination of size and detailed sampling of this dataset, we conclude by presenting a map showing in unprecedented detail the large-scale distribution of galaxies between 5 and 8 billion years.